Zobrazeno 1 - 10
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pro vyhledávání: '"Tidor, Jonathan"'
We study the number of monochromatic solutions to linear equations in a $2$-coloring of $\{1,\ldots,n\}$. We show that any nontrivial linear equation has a constant fraction of solutions that are monochromatic in any $2$-coloring of $\{1,\ldots,n\}$.
Externí odkaz:
http://arxiv.org/abs/2410.13758
For $d\geq 2$ and any norm on $\mathbb R^d$, we prove that there exists a set of $n$ points that spans at least $(\tfrac d2-o(1))n\log_2n$ unit distances under this norm for every $n$. This matches the upper bound recently proved by Alon, Buci\'c, an
Externí odkaz:
http://arxiv.org/abs/2410.07557
Autor:
Tidor, Jonathan, Yu, Hung-Hsun Hans
We prove three main results about semialgebraic hypergraphs. First, we prove an optimal and oblivious regularity lemma. Fox, Pach, and Suk proved that the class of $k$-uniform semialgebraic hypergraphs satisfies a very strong regularity lemma where t
Externí odkaz:
http://arxiv.org/abs/2407.20221
Degeneracy plays an important role in understanding Tur\'an- and Ramsey-type properties of graphs. Unfortunately, the usual hypergraphical generalization of degeneracy fails to capture these properties. We define the skeletal degeneracy of a $k$-unif
Externí odkaz:
http://arxiv.org/abs/2401.00359
A graph is $H$-Ramsey if every two-coloring of its edges contains a monochromatic copy of $H$. Define the $F$-Ramsey number of $H$, denoted by $r_F(H)$, to be the minimum number of copies of $F$ in a graph which is $H$-Ramsey. This generalizes the Ra
Externí odkaz:
http://arxiv.org/abs/2312.06895
Ruzsa asked whether there exist Fourier-uniform subsets of $\mathbb Z/N\mathbb Z$ with density $\alpha$ and 4-term arithmetic progression (4-APs) density at most $\alpha^C$, for arbitrarily large $C$. Gowers constructed Fourier uniform sets with dens
Externí odkaz:
http://arxiv.org/abs/2307.06914
Autor:
Tidor, Jonathan
Fourier analysis has been used for over one hundred years as a tool to study certain additive patterns. For example, Vinogradov used Fourier-analytic techniques (known in this context as the Hardy-Littlewood circle method) to show that every sufficie
Externí odkaz:
https://hdl.handle.net/1721.1/145125
In this paper, we give a cubic Goldreich-Levin algorithm which makes polynomially-many queries to a function $f \colon \mathbb F_p^n \to \mathbb C$ and produces a decomposition of $f$ as a sum of cubic phases and a small error term. This is a natural
Externí odkaz:
http://arxiv.org/abs/2207.13281
Autor:
Tidor, Jonathan
Publikováno v:
Discrete Anal. 2022:14, 17 pp
This paper gives the first quantitative bounds for the inverse theorem for the Gowers $U^4$-norm over $\mathbb{F}_p^n$ when $p=2,3$. We build upon earlier work of Gowers and Mili\'cevi\'c who solved the corresponding problem for $p\geq 5$. Our proof
Externí odkaz:
http://arxiv.org/abs/2109.13108
Publikováno v:
Math. Proc. Cambridge Philos. Soc. 173 (2022), 525--537
In this note we characterize when non-classical polynomials are necessary in the inverse theorem for the Gowers $U^k$-norm. We give a brief deduction of the fact that a bounded function on $\mathbb F_p^n$ with large $U^k$-norm must correlate with a c
Externí odkaz:
http://arxiv.org/abs/2107.07495